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PROOF       continued ...




 Proofing
Proofs of the Sum and Difference Identities ...



               O               Rotate ∠ROP so that OP        O
                               lies on the positive x-axis
Proofs of the Sum and Difference Identities ...



       O               Rotate ∠ROP so that OP        O
                       lies on the positive x-axis
Recall the Even and Odd Identities
 The sine and tangent functions are ODD functions.
 Cosine is an EVEN function.
  sin(-x) = -sin(x)        cos(-x) = cos(x)          tan(-x) = -tan(x)
Recall the Even and Odd Identities
 The sine and tangent functions are ODD functions.
 Cosine is an EVEN function.
  sin(-x) = -sin(x)        cos(-x) = cos(x)          tan(-x) = -tan(x)
Now back to our regularly scheduled programming ...
How would you show this ...
Recall the Even and Odd Identities
 The sine and tangent functions are ODD functions.
 Cosine is an EVEN function.
  sin(-x) = -sin(x)        cos(-x) = cos(x)          tan(-x) = -tan(x)
     How would you show this ...
Given:   With   and

  Find
Given:   With   and

  Find
Prove the following identity ...
Prove:

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Pre-Cal 40S Slides October 26, 2007

  • 1. PROOF continued ... Proofing
  • 2. Proofs of the Sum and Difference Identities ... O Rotate ∠ROP so that OP O lies on the positive x-axis
  • 3.
  • 4. Proofs of the Sum and Difference Identities ... O Rotate ∠ROP so that OP O lies on the positive x-axis
  • 5. Recall the Even and Odd Identities The sine and tangent functions are ODD functions. Cosine is an EVEN function. sin(-x) = -sin(x) cos(-x) = cos(x) tan(-x) = -tan(x)
  • 6. Recall the Even and Odd Identities The sine and tangent functions are ODD functions. Cosine is an EVEN function. sin(-x) = -sin(x) cos(-x) = cos(x) tan(-x) = -tan(x)
  • 7. Now back to our regularly scheduled programming ...
  • 8. How would you show this ...
  • 9. Recall the Even and Odd Identities The sine and tangent functions are ODD functions. Cosine is an EVEN function. sin(-x) = -sin(x) cos(-x) = cos(x) tan(-x) = -tan(x) How would you show this ...
  • 10. Given: With and Find
  • 11. Given: With and Find
  • 12. Prove the following identity ...